Specification and Computation of Warping and Morphing Transformations. Bruno Costa da Silva Microsoft Corp.

Transcription

1 Specification and Computation of Warping and Morphing Transformations Bruno Costa da Silva Microsoft Corp.

2 Morphing Transformations Representation of Transformations Specification of Transformations Specification Techniques

3 Morphing Transformation Shape & Attribute Transformation Shape transformation Alignment Shape Combination Blending Attribute transformation Combination Input = two different graphical objects Output = a new graphical object 3

4 Morphing Input Aligned Output f 1 Warp W ( f ) 1 Combine g f 2 Warp W ( f ) 2 g = A ( W ( f ), W ( f )) 1 2 4

5 Example: Shape Transformation Alignment through Warping 5

6 Example: Attribute Transformation Cross-dissolve + = 6

7 Example: Morphing + = + = 7

8 Transformation Dimension Intrinsic Dimension of Objects: Letters are 2D Buildings are 3D Transformations can occur in: Intrinsic dimension Visualization dimension 8

9 2D x 3D Transformations 9

10 2D Warp x 3D Warp 10

11 Reduced Dimension Morphing 2.5D morphing 3D warp + 2D cross-dissolve View Morphing Infer projection parameters New views from other viewpoints 11

12 View Morphing 12

13 Transformations Animations Input graphical object: Static Dynamic Transformation: Fixed Variable Output graphical object: Dynamic 13

14 Producing Animations Input Static Transformation Fixed Output Static Static Variable Dynamic Dynamic Fixed Dynamic Dynamic Variable Dynamic 14

15 Morphing Transformations Representation of Transformations Specification of Transformations Specification Techniques

16 Abstraction Levels Physical Universe Mathematical Universe Representation Universe Implementation Universe 16

17 The Transformation Process User Specification Representation Results Computation 17

18 The Transformation Process Characteristics User Input: Short and simple Representation: Can be complex, but Simple to obtain from specification and Simple to use for computation 18

19 Selecting a Representation Goals Computer storage and manipulation Finiteness and continuity Control and user friendliness Possibility of efficient computation Simplicity 19

20 Representation Example Projective Warp A B B A D D C C 20

21 Representation Example Some Possible Decisions User Inputs: Perspective parameters Four corners and their deformation Representations: Four corners and their deformation Transformation matrix 21

22 Morphing Transformations Representation of Transformations Specification of Transformations Specification Techniques

23 Specifying Transformations Globally Few parameters Locally Large number of parameters Complex specification/computation Warping and Morphing 23

24 Examples Global Local 24

25 Specification Principles What happens to each point of the domain? Can be described: for every individual point (not feasible) for a few regions and interpolated indirectly through parameters 25

26 Examples Interpolated Parameters (80% of pinch) 26

27 Specification Definitions Correspondence association between two regions defines original and final states Specification set of correspondences 27

28 Specification Example Three Correspondences Original Set Final Set 28

29 Warping x Morphing Warping Single object Specification of original and deformed states Morphing Two objects Specification of initial and final states 29

30 Warping x Morphing Warping Morphing 30

31 Morphing Transformations Representation of Transformations Specification of Transformations Specification Techniques

32 Types of Specification Parametric Partition-based Feature-based Automatic or semi-automatic 32

33 Parametric Specification Controlled by few parameters Examples: rotation, twist, visualization 33

34 Specification by Partition Regions cover the entire object Regular x Irregular partitions Same topology: original and final sets 34

35 Partition Examples 35

36 Specification by Features Regions do not cover the object Dimension of features object dimension Examples: points, vectors, planes, boxes,... 36

37 Feature Examples 37

38 Automatic Specification No region correspondences Reduced specification (if any) Approaches: Automatic computation Automatic detection of object features Digitization (rotoscoping) 38

39 Automatic Example 39

40 Resulting Transformation Behavior in: Specified Areas close to specification Unspecified areas should maintain continuity close to expected behavior 40

41 Specification Goals Minimal input Predictable, common sense behavior Leads to Dualities: Specification x Computation Specified x Inferred Amount of input x Predictability 41

42 Next Comparison of specification techniques Videos Specification and computation duality Computation of transformations 42

43 Specification and Computation of Warping and Morphing Transformations (part II) Bruno Costa da Silva Microsoft Corp.

44 Specification + Computation Computation of Transformations Conclusion

45 Specification + Computation Specification techniques influence computation: Split responsibilities Specification-wise analysis Computation considered 45

46 Case Analysis Techniques and their specification Point-based Vector-based Spline mesh Feature-based spline mesh Drawing-based 46

47 Point-based + Simple interpolations Simple user interface Higher dimensions Different types of graphical objects May need many points Consistency problems Predictability Computation 47

48 Point-based Example 48

49 Vector Based + Few vectors needed Simple user interface Higher dimensions Different types of graphical objects Computation Consistency problems Predictability 49

50 Vector Based Example 50

51 Spline Mesh + Efficient multiple pass implementation Less consistency problems Predictability Higher dimensions Difficult specification User interface Restricted types of graphical objects Multiple pass anomalies 51

52 Spline Mesh Example 52

53 Feature-based Spline Mesh Feature specification Spline Computation User works with features Features deform spline meshes Spline meshes warp the objects 53

54 User Computation 54 Warp Grid Warp Grid Warp Grid Warp Object Warp Object Warp Object

55 Feature-based Spline Mesh + Feature specification Efficient spline mesh computation Higher dimensions Loose control Interpolation Consistency Restricted types of graphical objects Multi-pass anomalies 55

56 Feature-based Spline Mesh Example 56

57 Drawing Based + Flexible specification Rotoscoped features Different types of graphical object Computation Consistency problems Higher dimensions 57

58 Drawing-based Example 58

59 Specification + Computation Computation of Transformations Conclusion

60 Computation of Transformations Object representation Continuous x discrete Forward mapping Inverse mapping Multi-pass transformations 60

61 Forward Mapping Traverse input pixels Miss/overlap output pixels W p i p o Input Output 61

62 Inverse Mapping Traverse output pixels Does not waste work W -1 pi po Input Output 62

63 Forward Original Antialiased Inverse

64 Multi-pass Transformations Separable transformation T = f f f f 1 = f $ f $ f $ f n n Computation of f i simpler than T Efficient multi-pass computation 64

65 Multi-pass Transformations 65

66 Specification + Computation Computation of Transformations Conclusion

67 Specification Trends Minimization of user input favors: Feature specification Automatic feature extraction Automatic specification Efficiency favors: Partition based techniques (regularity) Simpler forms of interpolation 67

68 Conclusion Transformation Representation Importance of User and Specification Specification and Computation Duality Specification Techniques Comparison Simple Specification & Predictable Results 68